Question

The root-mean-square speed (thermal speed) for a certain gas at 100 degree C is 0.500 km/s. If the temperature of the gas is now increased to 200 degree C, the root-mean-square(thermal) speed will be closest to a.563 m/s. b.1000 m/s c.634m/s d.707 m/s e.804 m/s.

Answer 1

Answer:

Step-by-step explanation:

Root mean square speed (V) is directly proportional to √{T} where T is the temperature in KELVIN. The root mean square of a gas is given as Vrms = √(3RT/M) where T is the temperature in Kelvin.

So, we can write (V1/V2) = √{T1/T2}

the temperature is being changed from 100 degree celsius or 373.15 kelvin to 200 degree celsius or 473.15 kelvin.

V1=.500Km/s=500m/s, T1=273+100=373K

T2=273+200=473K

From V2 = V1√{T2/T1}

Plugging the values

V2=500sqrt{473/373} = 563m/s.

Hence, the root-mean-square(thermal) speed will be closest to 563 m/s